No, it is rare for a business to ask a city for permission. However, choosing a geographically descriptive name may cause you to be unable to effectively protect your business name against adoption of very similar names by others. For example, Boston Group. There could be such a group in other Bostons or by any number of people named Boston. My thought is you should pick a more distinctive name unless for your business the local connection is the key. Once the name is used exclusively and prominently by one company for a long time, it is possible the name will become primarily distinctive for goods or services of that company. Boston Market is an example, as are the various sports team such as the reigning world champions of baseball. But, that takes years of effort and lots of money for advertising.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
Q: "Can I use the name of a city in my website address or business entity name?"
R: Yes. Doing so is very, very common. When choosing a name for your company you'll need to consult with a trademark attorney who's licensed to practice in your state in order to understand the pros and cons of using a city name as part of your company name and to then "clear the rights" to the name you ultimately select. Good luck.
The above response is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
My colleagues offered good insights here. Using the name of city in your domain is fine, but as noted, it could be problematic from a trademark perspective; it frankly depends.
Whenever you endeavor into investing in a trademark it is very important that you conduct the proper clearance due diligence upfront and before you submit an application to the USPTO. In the US, this means searching under both federal (USPTO) as well as common law because trademark rights stem from use in this country NOT registration. This means that acquiring a federal registration does not necessarily mean that you are not infringing on another's intellectual property. See the link below for a detailed explanation of the due diligence process.
I suggest that you consult with a lawyer in private and discuss your objectives in more detail. You can start by calling around to several for a free phone consultation, get some insights then pick the best fit to work with.
DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed with the law firm of Natoli-Lapin, LLC on the basis of this posting.
To answer the specific question, the answer is "yes". As others have noted, you can use the name, and you don't need permission from the city or town (unless you are trying to pass yourself off as an "official" government entity, which is a no-no.)
There are reasons, however, as the others have alluded to, why it might not make sense, if such a name is 'merely' descriptive of where your business is. E.g., "The Wellesley Inn" (formerly) in Wellesley Square, chose the name as a description of where the business was located. It could not bar another business from using "Wellesley Inn and Suites" elsewhere in the country, and it also didn't try to bar the "Wellesley Motor Inn" from operating with that name. Likewise, food producers using the name "Wellesley" or "Nantucket" chose the name for certain products (e.g., certain types of cookies) to connote quality (versus e.g. Cisco Brewery - location).
You should speak with an attorney before choosing a name, but also "Google" the name before you speak with an attorney - you'd prefer to stand out, and not start out in conflict with another business which has the same name.